Question

(3.3.25) Use the following cell phone airport data speeds​ (Mbps) from a particular network. Find P40.
0.1
0.2
0.3
0.5
0.6
0.6
0.7
0.7
0.8
0.8
0.8
0.8
0.8
0.9
0.9
1.3
1.4
1.5
1.6
1.6
1.6
2.1
2.1
2.4
2.4
2.5
3.4
3.6
4.1
4.2
4.5
4.6
5.7
6.7
7.7
8.1
8.5
12.6
12.6
12.8
12.8
13.3
13.3
13.7
14.2
14.3
15.1
15.5
15.6
28.6
P40=? Mbps

Answer 1

The data are in ascending order.

Compute the position of the p^th percentile (index $i$ ):

$$i=\dfrac{p}{100}\times n=\dfrac{40}{100}\times50=20$$

The index $i$  is an integer ⇒ the 40^th percentile is the average of the values in the 19^th and 20^th positions (1.6 and 1.6 respectively)

Answer: the 40^th percentile is (1.6 + 1.6) / 2 = 1.6

P40=1.6 Mbps